Math 2121 (Fall 2017)

Welcome to the homepage for Math 2121: Linear algebra!

• Send questions for the instructor to emarberg@ust.hk.
• Send questions about grades to your TA.

Check out the syllabus here.

Lectures:

• L1: Mondays 3:00-4:20PM and Fridays 10:30-11:50AM, Lecture Theater D
• L2: Tuesdays and Thursdays 9:00-10:20AM, Lecture Theater B

Office hours:

Room 3492, Lift 25-26.
Drop by anytime, or send me an email to make an appointment.

Textbooks:

• Linear Algebra and its Applications, 5th edition, by D. Lay, S. Lay, and J. McDonald
• Linear Algebra Done Right by Axler

Grading:

• 10%: homework assignments, weighted equally
• 30%: midterm examination
• 60%: final examination

Miderm:

• The midterm will be held on 21 October from 3:00 PM to 5:00 PM.
• Email the instructor right away if you have a conflict with this time.
• Midterm locations:
  • L1: Lecture Theater J
  • L2 (even student ID): Lecture Theater E
  • L2 (odd student ID): Classroom 4621
• The midterm will cover Lectures 1-12 and HW 1-6.
• Practice midterm [solutions]
• Solutions to the midterm

Final:

• The final examination will be held on 13 December from 12:30 PM to 3:30 PM.
• There will be no alternate exam times.
• For the location of the final, check here.
• The final will cover Lectures 1-24 and all homework assignments.
• Practice final [solutions]

Schedule:

• Week 1: Linear systems, row reduction to echelon form (reading: Sections 1.1-1.2)
• Week 2: Vectors, matrix equations, linear independence (reading: Sections 1.3-1.5, 1.7)
• Week 3: Matrices as linear transformations, applications (reading: Sections 1.8-1.10)
• Week 4: Matrix multiplication, the inverse of a matrix (reading: Sections 2.1-2.3)
• Week 5: Subspaces, null and column space, dimension (reading: Sections 2.4, 2.8-2.9)
• Week 6: Determinants (reading: Sections 3.1-3.2)
• Week 7: Vector spaces, eigenvectors, and eigenvalues (reading: Sections 4.1-4.6, 5.1)
• Week 8: Similarity and diagonalisable matrices (reading: Sections 5.2-5.4)
• Week 9: Complex eigenvalues, properties of eigenvalues (reading: Sections 5.5, 6.1)
• Week 10: Inner products, orthogonality, and projections (reading: Sections 6.1-6.3)
• Week 11: Gram-Schmidt process, least-squares problems (reading: Sections 6.4-6.6)
• Week 12: Symmetric matrices, singular value decompositions (reading: Sections 7.1, 7.4)

Lectures:

• Lecture 1: Systems of linear equations
• Lecture 2: Row reduction to echelon form
• Lecture 3: Vectors in Euclidean space
• Lecture 4: Matrix-vector products, linear independence
• Lecture 5: The matrix of a linear transformation
• Lecture 6: One-to-one and onto functions, electrical networks
• Lecture 7: Matrix operations, matrix multiplication
• Lecture 8: Invertible functions and matrices
• Lecture 9: Subspaces, null and column space of a matrix
• Lecture 10: Dimension and rank
• Lecture 11: Introduction to the determinant
• Lecture 12: Properties of the determinant
• Lecture 13: Midterm review
• Lecture 14: Vector spaces
• Lecture 15: Eigenvectors and eigenvalues
• Lecture 16: Similar and diagonalisable matrices
• Lecture 17: Fibonacci numbers and repeated eigenvalues
• Lecture 18: Complex eigenvalues
• Lecture 19: Eigenvalues, inner products and orthogonality
• Lecture 20: Orthogonal vectors and orthogonal projections
• Lecture 21: More on projections, the Gram-Schmidt process
• Lecture 22: Least-squares solutions
• Lecture 23: Symmetric matrices
• Lecture 24: Singular value decompositions
• Lecture 25: Final review

Assignments:

Homework will be submitted online using WeBWorK.
Assignments will be due at midnight each Wednesday.

• First homework assignment due on 13 September.
• No homework due on 25 October.
• Last homework assignment due on 29 November.